Rémi Avriller

Electron-phonon interaction and full counting statistics in molecular junctions

The full counting statistics of a molecular level weakly interacting with a local phonon mode is derived. We find an analytic formula that gives the behavior of arbitrary irreducible moments of the distribution upon phonon excitation. The underlying competition between quasielastic and inelastic processes results in the formation of domains in parameter space characterized by a given sign in the jump of the irreducible moments. In the limit of perfect transmission, the corresponding distribution is distorted from Gaussian statistics for electrons to Poissonian transfer of holes above the inelastic threshold.

LOW-DIMENSIONAL QUANTUM TRANSPORT PROPERTIES OF CHEMICALLY-DISORDERED CARBON NANOTUBES: FROM WEAK TO STRONG LOCALIZATION REGIMES

In this review, the quantum transport of nitrogen-doped metallic carbon nanotubes under magnetic field are explored. An accurate modeling of chemical disorder effects is derived from ab initio calculations. General properties for low bias Landauer conductance are investigated in the coherent regime, which enlighten the strong interplay between band structure and quantum interference effects. Characteristic transport length scales such as the elastic mean free path and localization length are extracted from phenomenological laws as well as scaling features with nanotube radius and doping level. The statistical analysis of conductance properties allow us to study the transition between weak and strong localization regimes.

Nonlinear effects of phonon fluctuations on transport through nanoscale junctions

We analyze the effect of electron-phonon coupling on the full counting statistics of a molecular junction beyond the lowest order perturbation theory. Our approach allows to take into account analytically the feedback between the nonequilibrium phonon and electronic distributions in the quantum regime. We show that for junctions with high transmission and relatively weak electron-phonon coupling this feedback gives rise to increasingly higher nonlinearities in the voltage dependence of the cumulants of the transmitted charges distribution.

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical results are obtained in the regime of very short times. We study in particular the apparent bistable behavior occurring for strong electron-phonon coupling, small bias voltages and a detuned dot level. The results obtained are in remarkable good agreement with numerically exact results obtained by Quantum Monte Carlo methods. We analyze the waiting time distribution and charge transfer probabilities, showing that only a single electron transfer is responsible for the rich structure found in the short times regime. A universal scaling (independent of the model parameters) is found for the relative amplitude of the higher order current cumulants in the short times regime, starting from an initially empty dot. We finally analyze the convergence to the steady state of the differential conductance and of the differential Fano factor at the inelastic threshold, which exhibits a peculiar oscillatory behavior.

Inelastic shot noise characteristics of nanoscale junctions from first principles

We describe an implementation of ab-initio methodology to compute inelastic shot noise signals due to electron-vibration scattering in nanoscale junctions. The method is based on the framework of non-equilibrium Keldysh Greens functions with a description of electronic structure and nuclear vibrations from density functional theory. Our implementation is illustrated with simulations of electron transport in Au and Pt atomic point contacts. We show that the computed shot noise characteristics of the Au contacts can be understood in terms of a simple two-site tight-binding model representing the two apex atoms of the vibrating nano-junction. We also show that the shot noise characteristics of Pt contacts exhibit more complex features associated with inelastic interchannel scattering. These inelastic noise features are shown to provide additional information about the electron-phonon coupling and the multichannel structure of Pt contacts than what is readily derived from the corresponding conductance characteristics. We finally analyze a set of Au atomic chains of different lengths and strain conditions and provide a quantitative comparison with the recent shot noise experiments reported by Kumar et al. [Phys. Rev. Lett. 108, 146602 (2012)].

Unified description of charge transfer mechanisms and vibronic dynamics in nanoscale junctions

We propose a general framework that unifies the description of counting statistics of transmitted (fermionic) charges as it is commonly used in the quantum transport community with the description of counting statistics of phonons (bosons). As a particular example, we study on the same footing the counting statistics of electrons transferred through a molecular junction and the corresponding population dynamics of the associated molecular vibrational mode. In the tunnel limit, non-perturbative results in the electron-phonon interaction are derived that unify complementary approaches based on rate equations or on the use of non-equilibrium Green functions.

Andreev bound-state dynamics in quantum-dot Josephson junctions: a washing out of the 0-π transition.

We consider a Josephson junction formed by a quantum dot connected to two bulk superconductors in presence of Coulomb interaction and coupling to both an electromagnetic environment and a finite density of electronic quasi-particles. In the limit of large superconducting gap we obtain a Born-Markov description of the system dynamics. We calculate the current-phase relation and we find that the experimentally unavoidable presence of quasi-particles can dramatically modify the 0-π standard transition picture. We show that photon-assisted quasi-particles absorption allows the dynamic switching from the 0to the π-state and vice-versa, washing out the 0-π transition predicted by purely thermodynamic arguments.

Mechanical Signatures of the Current Blockade Instability in Suspended Carbon Nanotubes.

Transport measurements allow sensitive detection of nanomechanical motion of suspended carbon nanotubes. It has been predicted that when the electromechanical coupling is sufficiently large a bistability with a current blockade appears. Unambiguous observation of this transition by current measurements may be difficult. Instead, we investigate the mechanical response of the system, namely, the displacement spectral function, the linear response to a driving, and the ring-down behavior. We find that by increasing the electromechanical coupling the peak in the spectral function broadens and shifts at low frequencies while the oscillator dephasing time shortens. These effects are maximum at the transition where nonlinearities dominate the dynamics. These strong signatures open the way to detect the blockade transition in devices currently studied by several groups.

Electromechanical transition in quantum dots

The strong coupling between electronic transport in a single-level quantum dot and a capacitively coupled nano-mechanical oscillator may lead to a transition towards a mechanically-bistable and blocked-current state. Its observation is at reach in carbon-nanotube state-of-art experiments. In a recent publication [Phys. Rev. Lett. 115, 206802 (2015)] we have shown that this transition is characterized by pronounced signatures on the oscillator mechanical properties: the susceptibility, the displacement fluctuation spectrum and the ring-down time. These properties are extracted from transport measurements, however the relation between the mechanical quantities and the electronic signal is not always straightforward. Moreover the dependence of the same quantities on temperature, bias or gate voltage, and external dissipation has not been studied. The purpose of this paper is to fill this gap and provide a detailed description of the transition. Specifically we find: (i) The relation between the current-noise and the displacement spectrum. (ii) The peculiar behavior of the gate-voltage dependence of these spectra at the transition. (iii) The robustness of the transition towards the effect of external fluctuations and dissipation.

Detection of ultrafast oscillations in superconducting point contacts by means of supercurrent measurements

We present a microscopic calculation of the nondissipative current through a superconducting quantum point contact coupled to a mechanical oscillator. Using the non-equilibrium Keldysh Green function approach, we determine the current-phase relation. The latter shows that at certain phases, the current is sharply suppressed. These dips in the current-phase relation provide information about the oscillating frequency and coupling strength of the mechanical oscillator. We also present an effective two-level model from which we obtain analytical expressions describing the position and width of the dips. Our findings are of relevance for nanomechanical resonators based on superconducting materials.